Spectral Efficiency Centrality: An Efficient Spectral Approach for Influential Node Identification in Temporal Networks

2026-08-14

AI Summary

This study addresses the challenge of balancing global structural analysis with computational efficiency in identifying critical nodes within temporal networks. We propose the Spectral Efficiency Centrality (SEC) framework and its approximation algorithm, ASEC. This work pioneers the extension of spectral node removal to temporal networks by leveraging Perron-Frobenius theory and first-order eigenvalue perturbation. By quantifying node importance through the impact of removal on the spectral radius of temporal snapshots, the method effectively avoids repetitive matrix decomposition. Experiments demonstrate that SEC significantly outperforms existing baselines across various propagation models. Furthermore, ASEC substantially enhances computational efficiency for large-scale networks, achieving both precise and scalable identification of critical nodes in dynamic systems.

Abstract

Centrality measures play a vital role in identifying influential nodes in evolving networks. While existing temporal centrality measures primarily rely on local structural properties or temporal paths, spectral node-removal approaches have been largely limited to static networks. To bridge this gap, we propose Spectral Efficiency Centrality (SEC), a temporal spectral centrality framework that quantifies node importance by evaluating the change in spectral radius caused by node removal across temporal snapshots. By capturing the global structural influence of nodes throughout network evolution, SEC identifies nodes that are critical for preserving the structural connectivity and efficiency of temporal networks. To improve computational scalability, we further develop an efficient approximation, ASEC, based on Perron-Frobenius theory and first-order eigenvalue perturbation. ASEC requires only the leading eigenpair and avoids repeated eigendecomposition, making it suitable for large temporal networks. Extensive experiments on multiple real-world temporal datasets demonstrate that SEC and ASEC outperform existing baseline centrality measures in identifying influential nodes under SI, SIS, and IC diffusion models. Statistical significance and robustness analyses further confirm their effectiveness, while ASEC offers a computationally efficient solution for large-scale temporal networks.

Problem

• Temporal Networks
• Influential Node Identification
• Spectral Centrality
• Node Importance
• Network Connectivity

Innovation

• Spectral Efficiency Centrality
• Temporal Networks
• ASEC Approximation
• Eigenvalue Perturbation
• Influential Node Identification